Finite Group Databasebeta

D59×#2009 #28615686

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD59×#2009

Splittings

FittingC59×#2009 ⋊ C2
SylowC59 ⋊ C2×#2009

Subgroups

subgroupG/H
centerC2#392×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2009C2
socleC2×C59C2×#392
prime radical#575×D59C2
hypercenter#2009D59
hypocenterC59C2×#2009
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2009

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

713 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 196565);